APY Calculator

How to Use the APY Calculator

APY answers one question: if I leave money in this account for a year and touch nothing, what percentage will it have grown by? That is the only rate on which two savings accounts can be compared fairly.

1. Enter the nominal annual rate. The headline figure, before compounding. If your provider only publishes an APY or AER, that number already includes compounding and does not need this tool.
2. Choose the compounding frequency. How often interest is added to the balance rather than merely accrued. Monthly is the most common; some accounts compound daily and credit monthly.
3. Enter a balance. Optional in spirit — it does not change the percentages, but it turns them into money, which is usually more persuasive than a fourth decimal place.
4. Read the table. It runs your rate at every frequency at once, so you can see the whole range from yearly to daily in one glance.

The gap between nominal and APY is small at ordinary savings rates and grows quickly at high ones. That matters more for borrowing than saving: a 21.9% card APR compounded monthly is an effective 24.24%.

APY Formula

One line, and the whole idea is in the exponent.

The reason APY exceeds the nominal rate is simple: interest credited in month one earns interest for the remaining eleven months. The more often it is credited, the more of the year it spends earning — but the extra months get shorter, which is why the gains taper off so sharply.

The taper is worth seeing in the numbers. Moving from yearly to quarterly compounding at 5.5% adds 0.1145 percentage points. Quarterly to monthly adds 0.0263. Monthly to daily adds 0.0128. Each step gives roughly a quarter of what the previous one did, and the whole series converges on the continuous limit of 5.6541%. There is a ceiling, and it sits barely above the daily figure.

Example

5.5% nominal, compounded monthly, on $25,000

1. Rate per period: 0.055 ÷ 12 = 0.00458333.
2. Growth over twelve periods: 1.00458333¹² = 1.056408.
3. Subtract one: 0.056408, or 5.6408% APY.
4. Interest in year one: 25,000 × 0.056408 = $1,410.20.
5. Without compounding: 25,000 × 0.055 = $1,375.00. Compounding is worth $35.20 on this balance.

The same 5.5% at every frequency

From yearly to daily is worth $38.40 on $25,000 — about 0.15% of the balance. Choosing an account 0.2 percentage points higher on the nominal rate would have been worth $50. Frequency is the smaller lever by some distance.

Which Account Actually Pays More

APY earns its keep when the two accounts you are comparing quote differently.

Account A has the highest advertised rate and the lowest yield. B wins, by four hundredths of a point over C. On $25,000 that is about $10 a year — which tells you something else worth knowing: once you have converted everything to APY, the remaining differences at ordinary savings rates are usually trivial, and access terms, deposit protection and whether the rate is introductory matter more.

The picture reverses for debt. At 21.9% compounded monthly, the effective rate is 24.24% — a gap of 2.34 points rather than 0.14. High rates make compounding frequency matter, which is why credit card arithmetic punishes delay so heavily. The credit card interest calculator shows what that does to a real balance.

There is a second reason to think in APY rather than nominal rates, and it is about how offers are presented. A provider quoting a nominal rate compounded yearly and one quoting a nominal rate compounded daily are describing different products with the same-looking number. Regulators in many markets require the effective figure — APY in the United States, AER in the United Kingdom — precisely so that the comparison cannot be gamed by choosing a flattering compounding convention.

The habit to build is simple. Whenever you see an interest rate quoted anywhere, ask two questions before comparing it with anything: is this nominal or effective, and over what period does it compound? Those two answers turn every rate you encounter into the same currency, and this calculator does the conversion in one step once you know them.

Three Things to Check Before Trusting a Yield

Three things to check before trusting a quoted yield.

Is it introductory? A 5.5% APY that reverts to 1.2% after twelve months is a 5.5% account for one year and a 1.2% account after that. Model the reversion rate for any money you will not move.

Is there a balance cap? Many headline rates apply only up to a ceiling — the first $5,000, say — with the excess earning a much lower rate. Your blended yield is then far below the advertised one.

Are there conditions? Minimum monthly deposits, no withdrawals, a linked current account. Missing a condition in one month often forfeits that month's bonus entirely, which costs more than any difference in compounding frequency.

Finally, remember that APY is a gross figure. Tax on interest, where it applies, comes off the top, and inflation comes off what is left. A 5.6408% APY with 3% inflation and 20% tax is about 1.5% in real terms — the inflation calculator does that second adjustment, and the compound interest calculator projects the balance forward once you have settled on a rate.

One numerical caution. At very high rates the difference between nominal and effective stops being a rounding detail. A 30% nominal rate compounded monthly is an effective 34.49%; compounded daily it is 34.97%. If you are ever comparing short-term credit, store card rates or anything quoted in the twenties and thirties, run the conversion before you decide which offer is worse — the ranking sometimes changes, and the amounts involved are not small.

Finally, a note on what APY does not tell you: liquidity. A five-year fixed bond at 5.8% APY beats an instant-access account at 5.6%, right up until the month you need the money and discover that breaking the term forfeits most of the interest that made it attractive. Yield is one axis; access is another, and for an emergency fund the second one wins.

To put the whole page in one sentence: the nominal rate is what a provider chose to advertise, and the APY is what the account does. Everything else on this page is commentary on that distinction — how big the gap gets, when it matters, and which conditions can make an impressive-looking yield deliver considerably less than it promises.